Context-free graph languages of bounded degree are generated by apex graph grammars

The apex graph grammars generate precisely the context-free graph languages of bounded degree, independently of whether one considers hyperedge replacement systems or (boundary or confluent) NLC or edNCE graph grammars. The main feature of apex graph grammars is that nodes cannot be passed from nonterminal to nonterminal. The proof is based on a normal form result for arbitrary hyperedge replacement systems that forbids passing chains. This generalizes Greibach Normal Form.     

Repetitiveness of languages generated by morphisms

We study the repetition of subwords in languages generated by morphisms. Fundamental to our approach is the notion of quasi-repetitive elements. Using these elements we present a new characterization for repetitive morphisms, from which we derive a simple proof for the fact that a D0L-language is repetitive if and only if it is strongly repetitive (Ehrenfeucht and Rozenberg, Inform. and Control 59 (1983) 13–35). From this proof we obtain a structurally simple polynomial-time algorithm for deciding whether such a language is repetitive. From further results on quasi-repetitive elements we obtain as a consequence a complete characterization for all those morphisms on a two-letter alphabet that are repetitive, a result which is closely related to a result of Séébold (Bull. EATCS 36 (1988) 137–151) on the D0L periodicity problem. Finally, we characterize those morphisms f on a two-letter alphabet, for which the language L(f) generated by f or the language SL(f) of subwords of L(f) are context-free or even regular.     

The complexity of ranking simple languages

Ranking is the problem of computing for an input string its lexicographic index in a given (fixed) language. This paper concerns the complexity of ranking. We show that ranking languages accepted by 1-way unambiguous auxiliary pushdown automata operating in polynomial time is inNC ⁽²⁾. We also prove negative results about ranking for several classes of simple languages.C is rankable in deterministic polynomial time iffP=P ^#P , whereC is any of the following six classes of languages: (1) languages accepted by logtime-bounded nondeterministic Turing machines, (2) languages accepted by (uniform) families of unbounded fan-in circuits of constant depth and polynomial size, (3) languages accepted by 2-way deterministic pushdown automata, (4) languages accepted by multihead deterministic finite automata, (5) languages accepted by 1-way nondeterministic logspace-bounded Turing machines, and (6) finitely ambiguous linear context-free languages.This research was partially supported by the National Science Foundation under Grant DCR-8696097. A preliminary version of this paper was presented at the 3rd Annual Structure in Complexity Theory Conference, Washington, DC, June 1988.     

Context-free complexity of finite languages

In this paper the investigation of the theory of grammatical complexity as started by Bucher (1981) and Bucher, Culik II, Maurer and Wotschke (1981) is continued. The basic question we are concerned with is the following: Given some finite language L, what is the smallest number of context-free productions needed to generate L, the so-called (context-free) complexity of L. We strengthen some of the results given by Bucher et al. (1981), the main result being a necessary condition for certain sequences of finite languages to be of sublinear complexity.     

On the languages generated by context-sensitive fuzzy grammars

It is proved that the family of the languages generated by 1-fold fuzzy grammars with context-sensitive rules and grade larger than λ,0≦λ<1, is equal to the family of the context sensitive languages. Also, one shows that the family of the languages generated by fuzzy grammars with context-sensitive rules and grade larger than λ,0≦λ<1, is included in the family of the context-sensitive languages.     

Recognizability of graph and pattern languages

Graph language recognizability is defined and investigated by virtue of the syntactic magmoid, analogously with the syntactic monoid of a word language. In this setup, the syntax complexity of a given recognizable graph language can be determined, giving rise to a syntactic classification inside the class of recognizable graph languages.     

Affine moment invariants generated by graph method

The paper presents a general method of an automatic deriving affine moment invariants of any weights and orders. The method is based on representation of the invariants by graphs. We propose an algorithm for eliminating reducible and dependent invariants. This method represents a systematic approach to the generation of all relevant moment features for recognition of affinely distorted objects. We also show the difference between pseudoinvariants and true invariants.     

On languages generated by asynchronous spiking neural P systems

In this paper, we investigate the languages generated by asynchronous spiking neural P systems. Characterizations of finite languages and recursively enumerable languages are obtained by asynchronous spiking neural P systems with extended rules. The relationships of the languages generated by asynchronous spiking neural P systems with regular and non-semilinear languages are also investigated.     

Comparative complexity of the representation of languages by probabilistic automata

We analyze the effect of the degree of isolation of a cut point on the number of states P(U, ) of a probabilistic automaton representing the language U. We give an example of a language Uⁿ consisting of words of length n such that there exist numbers < for which P(Uⁿ, )/P(Uⁿ, )0 as n.Translated from Kibernetika, No. 3, pp. 21–25, May–June, 1989.     

The complexity of comparability graph recognition and coloring

Using the notion ofG-decomposition introduced in Golumbic [8, 9], we present an implementation of an algorithm which assigns a transitive orientation to a comparability graph inO(δ·|E|) time andO(|E|) space where δ is the maximum degree of a vertex and |E| is the number of edges. A quotient operation reducing the graph in question and preservingG-decomposition and transitive orientability is shown, and efficient solutions to a number ofNP-complete problems which reduce to polynomial time for comparability graphs are discussed.     

On the structure of node-label-controlled graph languages

A new kind of graph grammars (called NLC grammars) is introduced. The main theorem is a result on the combinatorial structure of graph languages generated by NLC grammars; it resembles the pumping theorem for context-free string languages.     

Growth rates of complexity of power-free languages

We present a new fast algorithm for calculating the growth rate of complexity for regular languages. Using this algorithm we develop a space and time efficient method to approximate growth rates of complexity of arbitrary power-free languages over finite alphabets. Through extensive computer-assisted studies we sufficiently improve all known upper bounds for growth rates of such languages, obtain a lot of new bounds and discover some general regularities.     

Separating k-separated eNCE graph languages

An eNCE graph grammar is k-separated (k1) if the distance between any two nonterminal nodes in any of its sentential forms is at least k. Let SEP_k denote the class of graph languages generated by k-separated grammars. Then, SEP₁ (SEP₂) is the class of eNCE (boundary eNCE) graph languages, and so SEP₂SEP₁. Recently, Engelfriet (1991) showed that SEP₃SEP₂ and conjectured that, in fact, SEP_k+1SEP_k for each k 1. We prove this conjecture affirmatively.